In this paper we will classify graph groups with respect to the complexity of knapsack.
It turns out that for every graph group, knapsack is complete for one of the following three
complexity classes: \(\mathsf {TC}^0\) , \(\mathsf {LogCFL}\) , and \(\mathsf {NP}\) .
We assume that the reader has some basic knowledge in complexity theory, in particular
concerning the class \(\mathsf {NP}\) . In this next section, we briefly recall the definitions of the other
two classes, \(\mathsf {TC}^0\)  and \(\mathsf {LogCFL}\) ; further details can be found in [1]}.
